The Ski-Lift Pathway: Thermodynamically Unique, Biologically Ubiquitous

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The Ski-Lift Pathway Thermodynamically Unique,
Biologically Ubiquitous Goren GordonWeizmann
Institute of ScienceRehovot Avshalom C.
Elitzur www.a-c-elitzur.co.il
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Outline

• The Goal A Unified Physical Set of Principles
  Underlying all Forms of Life
• Entropy, Information and Complexity
• The new Question How do Transitions from
  High-to-High-Entropy States Take Place?
• The Ski-Lift Model

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Ordered, Random, Complex

• Measures of Orderliness
• Divergence from equiprobability (Gatlin) (Are
  there any digits in the sequence that are more
  common?)
• Divergence from independence (Gatlin) (Is there
  any dependence between the digits?)
• Redundancy (Chaitin) (Can the sequence be
  compressed into any shorter algorithm?)
• 33333333333333333333333333333333333333333333333333
  33333333333333333333333333333333333333333333333333
  
• 18602711949459557740388677065918738568698437862300
  90655440136901425331081581505348840600451256617983
  
• 12345678901234567890123456789012345678901234567890
  12345678901234567890123456789012345678901234567890
  
• 61803398874989484820458683436563811772030917980576
  28621354486227052604628189024497072072041893911374
  

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Sequence d is
highly informative
Sequence d is
complex
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Bennetts Measure of Complexity

• Given A sequences shortest algorithm, how much
  computation is needed to produce it from the
  algorithm, or conversely to compress it back into
  it?

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Complexity is not directly related to
Order/Entropy
complexity
High order
Low order
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Ordered, Random, Alive

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Maxwells Demon
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A Lawful Maxwells Demon in a Complex Environment

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A Lawful Maxwells Demon in a Complex Environment
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Interim Summary

• Thermodynamics offers a ubiquitous physical basis
  for the understanding of numerous biological
  phenomena, through the introduction of concepts
  like entropy/order, information and complexity.

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How does Complexity Emerge?And How is it
Maintained?
Disorder
Order
Information/Complexity
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The Hypothesis Ski-Lift
High Order
Requires Energy
Spontaneous
Low Order
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The Hypothesis Ski-Lift
High Order
Step 1 Use Ski-Lift, get to the top
Requires Energy
Spontaneous
X
Desired state
Low Order
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The Hypothesis Ski-Lift
High Order
Step 1 Use Ski-Lift, get to the top
Requires Energy
Spontaneous
Step 2 Ski down
X
Desired state
Low Order
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The Ski-Lift Conjecture Life approaches
complexity from above, i.e., from the
high-order state, and not from below, from the
low-order state. Though the former route seems to
require more energy, the latter requires
immeasurable information, hence unrealistic
energy.
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Dynamical evolution of complex states
How to reach a complex state?
Initial state at equilibrium (unknown, high
entropy) Final complex state, defined by
environment

1. Direct path
2. Probabilistic
3. Deterministic
4. Ski-lift theorem

Ski-lift
Entropy
Final state
Initial state
Direct path
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Definitions
? state N? equivalent microstates of
? Entropy of state S(?)log(N?)
Initial state, ?i high entropy,N?i À 1 Final
state, ?f high complexity, specific, S(?f)S(?i)

• Operations allowed
• S- Decrease entropy.
• Uncontrolled
• Energy cost E?S
• 2. T Transformation.
• Controlled, requires information
• Does not change entropy on average, ltS(T?)
  S(?)gt0
• Energy cost E?

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Numerical example
? a0a1a2.an
?i18602711949459557740 (or any other random
number)
?f61803398874989484820 (a specific, complex
number)
?order00000000000000000000
18602711949459557740

• Operations
• S- Decrease entropy.
• Uncontrolled.

E? S
10602001040050500740
E? S
00000000000000000000
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Numerical example
? a0a1a2.an
?i18602711949459557740 (or any other random
number)
?f61803398874989484820 (a specific, complex
number)
?order00000000000000000000

• Operations
• S- Decrease entropy.
• Uncontrolled
• 2. T Transformations.
• Addition.
• ltS(T?)-S(?)gt0
• due to symmetry

T1(4)(2)(0)(6).(1) T2(1)(7)(8)(3).(9
)
T1?I 50662711949459557741 T2?order178300000000
00000009
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Direct Path
Perform a transformation on the initial state to
arrive at the final state
T?i!?f (???)
Initial state unknown For each transformation
only one initial state transforms to final state
Hilbert Space
Initial state
Final state
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Direct Path Probabilistic
Perform a transformation on the initial state to
arrive at the final state
T?i!?f (???)
Initial state unknown For each transformation
only one initial state transforms to final state
Hilbert Space
Perform transformation once Energy
cost E? Probability of success P1/N?ie-S(?i
) 1
Initial state
Final state
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Direct Path Deterministic
Perform a transformation on the initial state to
arrive at the final state
T?i!?f (???)
Initial state unknown For each transformation
only one initial state transforms to final state
Hilbert Space
Repeat transformation until final state is
reached Probability of success P1 Average
energy cost E? eS(?i)À 1
Initial state
Final state
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Direct Path Information
Perform a transformation on the initial state to
arrive at the final state
T?i!?f
If one has information about initial
state IiS(?i) And information about final state
(environment) IfS(?f) Then can perform the
right transformation once Probability of
success P1 Energy cost E? Information
required IS(?i)S(?f)
Hilbert Space
Initial state
Final state
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Ski-lift Path
Two stages path
Stage 1 Increase order S-?i! ?order Ends with a
specific, known state Probability of success
P11 Energy cost E1S(?i)
Hilbert Space
Initial state
Final state
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Ski-lift Path
Two stages path
Stage 1 Increase order S-?i! ?order Ends with a
specific, known state Probability of success
P11 Energy cost E1S(?i)
Hilbert Space
Stage 2 Controlled transformation T?order!?f End
s with the specific, final state Probability of
success P21 Energy cost E2?
Initial state
Final state
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Ski-lift Path Information
Requires information on final state
(environment), in order to apply the right
transformation on ordered-state
Probability of success P1 Energy cost
Eski-liftS(?i)? Information required IS(?f)
Hilbert Space
Initial state
Final state
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Comparison between paths

• Direct Path
• Probabilistic
• Low probability
• Low energy
• Deterministic
• High probability
• High energy
• Information
• Requires much information
• Low energy

• Ski-lift
• Deterministic
• Controlled
• Reproducible
• Costs low energy
• Requires only environmental information

Ski-lift uses ordered-state and environmental
information to obtain controllability and
reproducibility
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What is life? revisited
Hilbert Space
Requires energy
High entropy High information
High order Redundancy
High complexity (specific environment)
Requires information
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Biological examples

• Cell formation
• Embryonic development
• Natural selection
• Ecological development

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Cell formation

• Initial state free molecules in primordial pool
• Ski-lift model
• 1. Increased order compartmentalization
• 2. Controlled transformation specialization
• Direct path
• Improbable, Irreproducible

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Embryonic development

• Initial state fertilized ovum nutrients
• Ski-lift model
• 1. Increased order mitosis, Blastocyte
• 2. Controlled transformation differentiation
• Direct path
• Differentiation to final organism
• Improbable, irreproducible due to high
• susceptibility to environmental variations

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The Morphotropic State as the Embryonic
Progenitor of Complexity

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The Morphotropic State as the Cellular Progenitor
of Complexity

• Minsky A, Shimoni E, Frenkiel-Krispin D. (2002)
  Stress, order and survival. Nat. Rev. Mol.
  Cell Biol. Jan3(1)50-60.

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Natural selection

• Initial state Individual resources
• Ski-lift model
• 1. Increased order reproduction
• 2. Controlled transformation minor mutations
• Direct path
• Large mutations. Attempts to reach optimized
  organism at one go.
• Improbable, irreproducible due to high
• susceptibility to environmental variations

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Ecological development

• Initial state Natural complexity
• Ski-lift model
• 1. Increased order accumulate resources
• 2. Controlled transformation build cities
• Direct path
• Develop technology without a controlled
  environment

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The Morphotropic State as the Ecological
Progenitor of Complexity